Title: Developing methods and software for fitting the Cox proportional hazards model to partly interval-censored data Abstract: Partly interval-censored time-to-event data arise frequently in medical studies for diseases that involve periodic examinations, such as cancer, HIV, infectious diseases, and diabetes. For example, progression-free survival (PFS), the most commonly used primary endpoint in phase III cancer clinical trials, is actually partly interval- censored as the time of death for a patient will be exactly known while the time of disease progression will be only known to fall between two imaging assessment timepoints. Due to the lack of well-developed methods and software, partly interval-censored data have been treated as right-censored data for analysis in clinical trials and medical studies, which introduces bias at the very beginning and may lead to invalid statistical inferences and erroneous medical conclusions. The proposed project contains four aims: (1) to develop a Bayesian semiparametric method for fitting the Cox proportional hazards model, the most commonly used survival regression model, to partly interval-censored data; (2) to develop a Bayesian semiparametric method for fitting the Cox proportional hazards model with spatial frailty to spatially correlated partly interval-censored data; (3) to develop a Bayesian semiparametric method for fitting a multiple-frailty proportional hazards model with frailty selection to clustered partly interval-censored data; (4) then based on the validated new methods, to construct an R package that is efficient, reliable, and user-friendly for medical investigators to use. R is the most used statistical computing and graphics software and is free to the public. Hence, such a tool will facilitate the search for effective new drugs and identification of risk factors, thereby lead to improvement in patient treatment and disease prevention for many diseases that are significantly affecting public health.